Dr. Bennet holds a PhD in physics from Stevens Institute, with specialization in General Relativity, and is the co-author of "Galileo Was Wrong".

I have interpolated explanatory comments where I thought they might be helpful.

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From the Planck survey the CMB has an average microwave background frequency f0m corresponding to2.72548 degs K in all directions. But when aimed at Leo the frequency increases slightly to f1, which is interpreted by the MS masters (consensus cosmology) as due to the motion of the Earth-Sun system at 378 km/s towards Leo, a blue-shift created as the Earth plows through the f0m background.

Df1 = f1–f0m, the increase in observed frequency in Leo’s direction.

The general Doppler shift for objects in relative motion is

f = (c+Vr)f0/(c-Vs)

where f is the measured freq, c the wave velocity, Vr and Vs the velocity of receiver and source, f0 the source freq.

For the MS (Mainstream) version of the CMB, Vr = Ve, the speed of the Earth through the background microwaves, the source is Leo at rest(Vs=0) and f = Df1.

So

Df1 = (c+Ve)f0m/c = (1+Ve/c)f0m

The two Radio Source surveys described in the paper perform another sky scan, but at lower radio frequencies. They find that the Leo direction again is a higher frequency, f2, than the average radio frequency background, f0r. Apply the same Doppler reasoning to the radio wave surveys...(of course the Earth’s speed relative to Leo remains the same):

Df2 = f2–f0r = (c+Ve)f0r/c = (1+Ve/c)f0r

Df, the Doppler freq shift, varies for the microwaves and radio waves.

But the paper reports that the measured frequency shifts of the micro and radio waves are the same!